Bond Energies in Molecules and Radicals

3 Energies of the Chemical Interaction of Atoms 2.3.1 Bond Energies in Molecules and Radicals 

Energy characteristics of atoms also define, to a large extent, the strengths of their bonds in molecules, polyatomic ions and radicals. The work required to disrupt a chemical bond, e.g. to separate chemically bonded atoms from the equilibrium distance to a practically infinite one (in the ground state) is called bond energy Eb). In case of the A2 and AX molecules, Eb is equal to the dissociation energy of the molecule (De) which can be determined by thermochemical, calorimetric, kinetic, mass-spectroscopic and molecular spectroscopic techniques. By definition, De characterizes atoms in molecules at the equilibrium state with zero-point energy, 

Thermochemical determinations of the bond energy are based on the measurements of the heats of reaction Q) at constant pressure 

Heats of reactions can be measured by the calorimetric and kinetic methods, using photo- and mass-spectrometry. Bond dissociation enthalpy calculated from the thermal effect of the reaction at ambient pressure is close to the bond energy because PV is small, for example for the hydrogen molecule PV 2.5 kJ/mol. Finally, the difference between the dissociation energy at 0 K and that at room temperature is also very small for the hydrogen molecule the difference is AE 1 kj/mol. 

From here, supposing m = 2n and thereby transforming the Mie equation into the Morse function (see Eq. 2.7) which describes energies of molecules very well, we finally obtain 

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